A comparison of techniques for the reconstruction of leaf surfaces from scanned data?

SIAM Journal on Scientific Computing

Volumn 36, Issue 6, 2014, Pages B969-B988

  Kempthorne, Daryl M ^a   Turner, Ian W ^a   Belward, John A ^a  

^a QUEENSLAND UNIVERSITY OF TECHNOLOGY   (Australia)

Author keywords

Finite element methods; Hsieh Clough Tocher methods; Surface smoothing; Virtual leaf construction

Indexed keywords

RADIAL BASIS FUNCTION NETWORKS; SILANES;

FLUID MOVEMENT; HSIEH-CLOUGH-TOCHE METHOD; LEAF SURFACES; MOVEMENT MODEL; PLANT ARCHITECTURE; SCANNING DEVICE; SCATTERED DATA; SURFACE FROM; SURFACE SMOOTHING; VIRTUAL LEAF CONSTRUCTION;

FINITE ELEMENT METHOD;

EID: 84919654309     PISSN: 10648275     EISSN: 10957197     Source Type: Journal    
DOI: 10.1137/130938761     Document Type: Article

References (24)

1. R. ARCANGÉLI, M. LÓPEZ DE SILANES, AND J. TORRENS, Multidimensional Minimising Splines, Springer, New York, 2004.
2. R. P. BRENT, Algorithms for Minimisation without Derivatives, Prentice-Hall, Englewood Cliffs, NJ, 1973.
3. G. DORR, J. HANAN, S. ADKINS, A. HEWITT, C. O'DONNELL, AND B. NOLLER, Spray deposition on plant surfaces: A modelling approach, Functional Plant Biology, 35(2008), pp. 988-996.
4. G. DORR, D. KEMPTHORNE, L. MAYO, W. FORSTER, J. ZABKIEWICZ, S. MCCUE, J. BELWARD, I. TURNER, AND J. HANAN, Towards a model of spray-canopy interactions: Interception, shatter, bounce and retention of droplets on horizontal leaves, Ecological Modelling, 290(2013), pp. 94-101.
5. G. DUPUIS AND J.-J. GÖEL, Finite element with high degree of regularity, Internat. J. Numer. Methods Engrg., 2(1970), pp. 563-577.
6. W. A. FORSTER, M. O. KIMBERLAY, AND J. A. ZABKIEWICZ, A universal spray droplet adhesion model, Trans. ASAE, 48(2005), pp. 1321-1330.
7. C. GEUZAINE AND J.-F. REMACLE, Gmsh: A 3-D finite element mesh generator with builtin pre- and post-processing facilities, Internat. J. Numer. Methods Engrg., 79(2009), pp. 1309-1331.
8. M. HUTCHINSON, A stochastic estimator of the trace of the influence matrix for Laplacian smoothing splines, Commun. Statist. Simul. Comput., 19(1990), pp. 433-450.
9. Intel Corporation, Product Export Compliance Metrics: Intel Core i7-2600 Desktop Processor Series, download.intel.com/support/processors/corei7/sb/core-i7-2600-d.pdf, 2012. Accessed Sept. 3, 2013.
10. D. M. KEMPTHORNE, I. W. TURNER, AND J. A. BELWARD, Computational strategies for surface fitting using thin plate spline finite element methods, ANZIAM J., 54(2013), pp. C56-C71.
11. B. LOCH, J. BELWARD, AND J. HANAN, Application of surface fitting techniques for the representation of leaf surfaces, in Proceedings of MODSIM05: International Congress on Modelling and Simulation, A. Zerger and R. Argent, eds., Modelling and Simulation Society of Australia and New Zealand, Melbourne, 2005, pp. 1272-1278.
12. B. I. LOCH, Surface Fitting for the Modelling of Plant Leaves, Ph. D. thesis, University of Queensland, Brisbane, Queensland, Australia, 2004.
13. T. A. MANTEUFFEL, An incomplete factorization technique for positive definite linear systems, Math. Comp., 34(1980), pp. 473-497.
14. M. N. OQIELAT, J. A. BELWARD, I. W. TURNER, AND B. I. LOCH, A hybrid Clough-Tocher radial basis function method for modelling leaf surfaces, in Proceedings of MODSIM07: International Congress on Modelling and Simulation, L. Oxley and D. Kulasiri, eds., Modelling and Simulation Society of Australia and New Zealand, Melbourne, 2007, pp. 400-406.
15. M. N. OQIELAT, I. W. TURNER, AND J. A. BELWARD, A hybrid Clough-Tocher method for surface fitting with application to leaf data, Appl. Math. Model., 33(2009), pp. 2582-2595.
16. M. N. OQIELAT, I. W. TURNER, J. A. BELWARD, AND S. W. MCCUE, Modelling water droplet movement on a leaf surface, Math. Comput. Simul., 81(2011), pp. 1553-1571.
17. S. ROBERTS, M. HEGLAND, AND I. ALTAS, Approximation of a thin plate spline smoother using continuous piecewise polynomial functions, SIAM J. Numer. Anal., 1(2003), pp. 208-234.
18. K. R. STERN, Introductory Plant Biology, 10th ed., McGraw-Hill, New York, 2006.
19. M. SUARJANA AND K. H. LAW, Successive conjugate gradient methods for structural analysis with multiple load cases, Internat. J. Numer. Methods Engrg., 37(1994), pp. 4185-4203.
20. M. E. TESKE, S. L. BIRD, D. M. ESTERLY, T. B. CURBISHLEY, W. L. RAY, AND S. G. PERRY, The splash/non-splash boundary upon a dry surface and thin fluid film, Experiments in Fluids, 40(2002), pp. 53-59.
21. A. N. TIKHONOV AND V. Y. ARSENIN, Solutions of Ill-posed Problems, John Wiley & Sons, New York, 1977.
22. U. TROTTENBERG, C. W. OOSTERLEE, AND A. SCHÜLLER, Multigrid, Academic Press, New York, 2000.
23. G. WAHBA, Spline Models for Observational Data, CBMS-NSF Reg. Conf. Ser. Appl. Math. 59, SIAM, Philadelphia, 1990.
24. W. L. WAN, T. F. CHAN, AND B. SMITH, An energy-minimizing interpolation for robust multigrid methods, SIAM J. Sci. Comput., 21(2000), pp. 1632-1649.